Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) | $X, Y : \Omega \to \Xi$ are each a D202: Random variable on $P$ |
(ii) | $\{ X \in E \}, \{ Y \in F \} \in \mathcal{F}$ are each an D1716: Event in $P$ |
Then
\begin{equation}
\mathbb{P}( X \in E, X = Y )
= \mathbb{P}( Y \in E, X = Y )
\end{equation}